I know the problem you are having and it is big a problem, because it's very possible you'd encounter the same problem even with a UPS that's just how the power supply in the PS3 is designed. It's very safe but the disadvantage is what you are experiencing it is VERY sensitive.
With the UPS, if it is the cheap ones that switches to battery power in loss of AC the same thing would happen as it may not switch in time to keep the PS3 on. (you would still get that delay.)
If it is a UPS that feeds the battery continuously and the battery feeds your devices you may have some more luck but depending on how much power the PS3 pulls you may get a small and temporary dip in voltage which may or may not cause the PS3's power supply safety features to kick in
